Fluorescence spectroscopy correlation function

We have done a study by time-resolved hole-burning spectroscopy for dye molecules in polar solvents and found that the time correlation function of the hole width decays much slower than that of the peak shift of the hole, which occurs very rapidly, as you observed in the case of the fluorescence Stokes shift [K. Nishiyama, Y. Asano, N. Hashimoto, and T. Okada, J. Mol. Liquids 65/66, 41 (1995)]. 

The arrival times of fluorescence photons contain information about correlations in fluorescence signals. Eluorescence correlation spectroscopy (FCS) (26) exploits these correlations to measure the magnitude and time scales of fluctuations in fluorescence. These fluctuations contain information about the dynamic time scales of the system and the concentration of fluorescing molecules. Correlations may span time ranges from nanoseconds to milliseconds, which extends the dynamic time window for fluorescence measurements far beyond what is achievable in fluorescence lifetime measurements. The autocorrelation function is calculated as ... 

In fluorescence correlation spectroscopy (FCS) a small volume element or a small area) of a sample is illuminated by a laser beam and the autocorrelation function of fluctuations in the fluorescence is determined by photon counting. From this autocorrelation function the mean number densities of the fluorophores and their diffusion coefficients can be extracted. Measurement and analysis of higher order correlation functions of the fluorescence has been shown to yield information concerning aggregation states of fluorophores ). 

In the previous sections, we derived general correlation function expressions for the nonlinear response function that allow us to calculate any 4WM process. The final results were recast as a product of Liouville space operators [Eqs. (49) and (53)], or in terms of the four-time correlation function of the dipole operator [Eq. (57)]. We then developed the factorization approximation [Eqs. (60) and (63)], which simplifies these expressions considerably. In this section, we shall consider the problem of spontaneous Raman and fluorescence spectroscopy. General formal expressions analogous to those obtained for 4WM will be derived. This will enable us to treat both experiments in a similar fashion and compare their information content. We shall start with the ordinary absorption lineshape. Consider our system interacting with a stationary monochromatic electromagnetic field with frequency w. The total initial density matrix is given by... 

In conclusion, in this section we presented the formal expressions for the absorption lineshape [Eq. (70)] and for spontaneous Raman and fluorescence spectroscopy. For the latter, we derived Liouville space expressions in the time and the frequency domain [Eqs. (74) and (75)], an ordinary correlation function expression [Eq. (76)], and, finally, the factorization approximation resulted in Eqs. (77) and (78). The factorization approximation is expected to hold in many cases for steady-state experiments and for time-resolved experiments with low temporal resolution. It is possible to observe a time-dependent shift of spontaneous emission lineshapes using picosecond excitation and detection [66-68]. This shift arises from the reorganization process of the solvent and also from vibrational relaxation that occurs during the t2 time interval. A proper treatment of these effects requires going beyond the... 

Fluorescence correlation spectroscopy r is used for the time in the correlation function. 

Fig. 3.4 Scheme of fluorescence correlation spectroscopy (FCS). In single (A) and dual (B) color FCS, the fluorescence in the observation volume of one (X) or two (X, Y) distinct classes of fluorophores, respectively, is monitored over time. The correlation functions are then used for the temporal analysis of the signals to determine the characteristic residence times of the labeled probes and their diffusion or binding constants. The correlation plots depict ideal cases. G(0) is the correlation amplitude, which is inversely proportional to the average number of fluorescent labels simultaneously present in the observation volume (N). 

There are, however, limits in the resolution of heterogeneous populations. In the particular case of multiple diffusing fluorescent species, for example in binding studies, the diffusion times must differ by a factor of 1.6-2.0 to be resolved, corresponding to a 4-8-fold increase in molecular weight. This limitation is alleviated in dual-color fluorescence cross-correlation spectroscopy (DC-FCCS) [116], in which the fluorescence fluctuation is simultaneously recorded in the same observation volume for two different species labeled with distinguishable fluorophores. The fraction of double-labeled and hence associated species is derived from the cross-correlation function between the two fluorescences (fig. 3.4B). 

In this chapter, we developed a stochastic theory of single molecule fluorescence spectroscopy. Fluctuations described by Q are evaluated in terms of a three-time correlation function C iXi, X2, T3) related to the response function in nonlinear spectroscopy. This function depends on the characteristics of the spectral diffusion process. Important time-ordering properties of the three-time correlation function were investigated here in detail. Since the fluctuations (i.e., Q) depend on the three-time correlation function, necessarily they contain more information than the line shape that depends on the one-time correlation function Ci(ti) via the Wiener-Khintchine theorem. 

Leonard (1977) traced the transformation sequence kaolinite-metakaolinite-spinel-muUite by studying the radial electron density (RED) distribution of kaolinite and its transition products as a function of temperature, and correlated the results with chemical information obtained with X-ray fluorescence spectroscopy. While the presence of some Si-Al spinel could not completely be ruled out, most of the A1 atoms were found in the configuration of y-Al203 beyond a firing temperature of 900°C. This assumption was corroborated by Sonuparlak et al. (1987), who showed by transmission electron microscopy (TEM) in conjunction with energy-dispersive X-ray (EDX) spectroscopy that the spinel phase formed at 980 °C, indicated by a strong exothermic DTA peak, contains <10 mass% Si02, if any. 

Inspection of Fig. 5.18 shows that the autocorrelation functions for this particular model decay exponentially with time, and that the rate constant for this decay is the sum of the rate constants for forward and backward transitions between the two states (kon + The upper curve in Fig. 5.18B, for example, decays to He (0.368) of its initial value in 16.61 At, which is the reciprocal of (0.05 -t 0.01 )Mt. In classical kinetics, if a system with first-order reactions in the forward and backward directions is perturbed by an abrupt change in the concentration of one of the components, a change in temperature, or some other disturbance, it will relax to equilibrium with a rate constant given by the sum of the rate constants for the forward and backward reactions. The fact that the autocorrelation functions in Fig. 5.18 decay with the relaxation rate constant of the system is a general property of classical time-correlation functions [259-262]. One of the potential strengths of fluorescence correlation spectroscopy is that the relaxation dynamics can be obtained with the system at equilibrium no perturbation is required. 

A useful and common way of describing the reorientation dynamics of molecules in the condensed phase is to use single molecule reorientation correlation functions. These will be described later when we discuss solute molecular reorientational dynamics. Indirect experimental probes of the reorientation dynamics of molecules in neat bulk liquids include techniques such as IR, Raman, and NMR spectroscopy. More direct probes involve a variety of time-resolved methods such as dielectric relaxation, time-resolved absorption and emission spectroscopy, and the optical Kerr effect. The basic idea of time-resolved spectroscopic techniques is that a short polarized laser pulse removes a subset of molecular orientations from the equifibrium orientational distribution. The relaxation of the perturbed distribution is monitored by the absorption of a second time-delayed pulse or by the time-dependent change in the fluorescence depolarization. 

In bulk isotropic media, experiments such as IR and NMR spectroscopy and fluorescence anisotropy decay can give information about these correlation functions or their moments.At an interface with a cylindrical symmetry, SHG and SFG spectroscopies give information about out-of-plane and in-plane reorientation, and they involve more complicated time correlation functions.Nonetheless, the simple C/(t) are still useful for a direct comparison between bulk and surface reorientation. 

Fluorescence intensity detected with a confocal microscope for the small area of diluted solution temporally fluctuates in sync with (i) motions of solute molecules going in/out of the confocal volume, (ii) intersystem crossing in the solute, and (hi) quenching by molecular interactions. The degree of fluctuation is also dependent on the number of dye molecules in the confocal area (concentration) with an increase in the concentration of the dye, the degree of fluctuation decreases. The autocorrelation function (ACF) of the time profile of the fluorescence fluctuation provides quantitative information on the dynamics of molecules. This method of measurement is well known as fluorescence correlation spectroscopy (FCS) [8, 9]. 

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